P
US8682059B2ActiveUtilityPatentIndex 62

Harmonic resist model for use in a lithographic apparatus and a device manufacturing method

Assignee: CAO YUPriority: Nov 24, 2008Filed: May 17, 2013Granted: Mar 25, 2014
Est. expiryNov 24, 2028(~2.4 yrs left)· nominal 20-yr term from priority
Inventors:CAO YUCHEN LUOQIBRUGUIER ANTOINE JEANSHAO WENJIN
G03F 7/70675G03F 7/70666G03F 7/705G06T 7/0004G06T 3/10
62
PatentIndex Score
2
Cited by
31
References
14
Claims

Abstract

A method for determining an image of a mask pattern in a resist coated on a substrate, the method including determining an aerial image of the mask pattern at substrate level; and convolving the aerial image with at least two orthogonal convolution kernels to determine a resist image that is representative of the mask pattern in the resist.

Claims

exact text as granted — not AI-modified
What is claimed is: 
     
       1. A method implemented by a computer processor for determining an image of a mask pattern in a resist coated on a substrate, the method comprising:
 determining, by the computer processor, an aerial image of the mask pattern at substrate level; and 
 transforming, by the computer processor, the aerial image into a resist image that is representative of the image of the mask pattern in the resist, the aerial image being transformed into the resist image using a model that includes at least two convolution kernels, the transforming including convolving the aerial image with the at least two convolution kernels, wherein the at least two convolution kernels are selected such that the transformation of the aerial image into the resist image has the properties of rotational and mirror symmetry conservation. 
 
     
     
       2. The method of  claim 1 , wherein the convolution kernels are orthogonal kernels. 
     
     
       3. The method of  claim 2 , wherein the convolution kernels are solutions of a two dimensional quantum harmonic oscillator. 
     
     
       4. The method of  claim 1 , wherein the resist image is represented by the following equation: 
       
         
           
             
               R 
               = 
               
                 
                   
                     ∑ 
                     
                       i 
                       = 
                       0 
                     
                     ∞ 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       c 
                       i 
                     
                     ⁡ 
                     
                       ( 
                       
                         A 
                         * 
                         
                           K 
                           i 
                         
                       
                       ) 
                     
                   
                 
                 + 
                 
                   
                     ∑ 
                     
                       i 
                       = 
                       0 
                     
                     ∞ 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         d 
                         i 
                       
                       ⁡ 
                       
                         ( 
                         
                           A 
                           * 
                           
                             K 
                             
                               1 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               i 
                             
                           
                         
                         ) 
                       
                     
                     · 
                     
                       ( 
                       
                         A 
                         * 
                         
                           K 
                           
                             2 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             i 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
       wherein R is a bitmap resist image, A is a bitmap aerial image of the mask pattern at substrate level, K i , K 1i , K 2i  are orthogonal convolution kernels and c i  and d i  are fitting coefficients, where 0≦i≦∞. 
     
     
       5. The method of  claim 1 , wherein the model includes a bilinear term that is the product between a first term and a second term, the first term corresponding to the convolution of the aerial image with a first orthogonal convolution kernel and the second term corresponding to the convolution of the aerial image with a second orthogonal convolution kernel. 
     
     
       6. The method of  claim 1 , wherein the computer processor comprises FPGA hardware. 
     
     
       7. The method of  claim 1 , wherein the computer processor comprises GPU-based hardware. 
     
     
       8. A non-transitory computer program product having machine executable instructions, the instructions being executable by a machine to perform a method for determining an image of a mask pattern in a resist coated on a substrate, the method comprising:
 determining an aerial image of the mask pattern at substrate level; and 
 transforming the aerial image into a resist image that is representative of the image of the mask pattern in the resist, the aerial image being transformed into the resist image using a model that includes at least two convolution kernels, the transforming including convolving the aerial image with the at least two convolution kernels, wherein the at least two convolution kernels are selected such that the transformation of the aerial image into the resist image has the properties of rotational and mirror symmetry conservation. 
 
     
     
       9. The computer program product of  claim 8 , wherein the convolution kernels are orthogonal kernels. 
     
     
       10. The computer program product of  claim 9 , wherein the convolution kernels are solutions of a two dimensional quantum harmonic oscillator. 
     
     
       11. The computer program product of  claim 8 , wherein the resist image is represented by the following equation: 
       
         
           
             
               R 
               = 
               
                 
                   
                     ∑ 
                     
                       i 
                       = 
                       0 
                     
                     ∞ 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       c 
                       i 
                     
                     ⁡ 
                     
                       ( 
                       
                         A 
                         * 
                         
                           K 
                           i 
                         
                       
                       ) 
                     
                   
                 
                 + 
                 
                   
                     ∑ 
                     
                       i 
                       = 
                       0 
                     
                     ∞ 
                   
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         d 
                         i 
                       
                       ⁡ 
                       
                         ( 
                         
                           A 
                           * 
                           
                             K 
                             
                               1 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               i 
                             
                           
                         
                         ) 
                       
                     
                     · 
                     
                       ( 
                       
                         A 
                         * 
                         
                           K 
                           
                             2 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             i 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
       wherein R is a bitmap resist image, A is a bitmap aerial image of the mask pattern at substrate level, K i , K 1i , K 2i  are orthogonal convolution kernels and c i  and d i  are fitting coefficients, where 0≦i≦∞. 
     
     
       12. The computer program product of  claim 8 , wherein the model includes a bilinear term that is the product between a first term and a second term, the first term corresponding to the convolution of the aerial image with a first orthogonal convolution kernel and the second term corresponding to the convolution of the aerial image with a second orthogonal convolution kernel. 
     
     
       13. The computer program product of  claim 8 , wherein the transforming is carried out using a FPGA hardware. 
     
     
       14. The computer program product of  claim 8 , wherein the transforming is carried out using GPU-based hardware.

Cited by (0)

No later patents cite this yet.

References (0)

No backward citations on record.